DAVID BORWEIN at NINETY

a tribute, archive & biography




1950


On the Cesàro summability of integrals

David Borwein

J. London Math. Soc., 25, 289-302, 1950

A summability factor theorem

David Borwein

J. London Math. Soc., 25, 302-315, 1950

1951


On the absolute Cesàro summabilty of integrals

David Borwein

Proc. London Math. Soc., (3)1, 308-326, 1951

1954


Note on summability factors

David Borwein

J. London Math. Soc., 29, 198-206, 1954

Integration by parts of Cesàro summable integrals

David Borwein

J. London Math. Soc., 29, 276-292, 1954

On the absolute summability of Stieltjes integrals

David Borwein

J. London Math. Soc., 29, 476-486, 1954

1955


On the abscissae of summability of a Dirichlet series

David Borwein

J. London Math. Soc., 30, 68-71, 1955

1956


A theorem on Riesz summability

David Borwein

J. London Math. Soc., 31, 319-324, 1956

1957


On a scale of Abel-type summability methods

David Borwein

Proc. Camb. Phil. Soc., 53, 318-322, 1957

On methods of summability based on power series

David Borwein

Proc. Royal Soc. Edinburgh, 64, 342-349, 1957

1958


A logrithmic method of summability

David Borwein

J. London Math. Soc., 33, 212-220, 1958

On products of sequences

David Borwein

J. London Math. Soc., 33, 352-357, 1958

Theorems on some methods of summability

David Borwein

Quart. J. Math. Oxford, (2)9, 310-316, 1958

On multiplication of (C, - $\mu$) summable series

David Borwein

J. London Math. Soc., 33, 441-449, 1958

On Borel-type methods of summability series

David Borwein

Mathematika, 5, 128-133, 1958

1959


On methods of summability base integral functions

David Borwein

Proc. Camb. Phil. Soc., 55, 23-30, 1959

Binary and ternary transformations of sequences

Joint with A. V. Boyd

Proc.Edinburgh Math. Soc., 11, 175-181, 1959

On finite difference solutions of two point boundary value problems

Joint with A. R. Mitchell

Zamp , 10, 221-232, 1959

An extension of a theorem on the equivalence between absolute Riezian and absolute Cesaro summability

David Borwein

Proc. Glasgow Math. Assoc., 4, 81-83, 1959

1960


Relations between Borel-type methods of summabilty

David Borwein

J. London Math. Soc., 35, 65-70, 1960

On moment constant methods of summability

David Borwein

J. London Math. Soc., 35, 71-77, 1960

On methods of summability base integral functions II

David Borwein

Proc. Camb. Phil. Soc., 56, 125-131, 1960

On strong and absolute summability

David Borwein

Proc. Glasgow Math. Assoc., 4, 122-139, 1960

Norlund methods of summability associated with polynomials

David Borwein

Proc.Edinburgh Math. Soc., 12, 7--15, 1960

1962


On Riesz summability factors

Joint with B. L. R. Shawyer

Proc. Glasgow Math. Assoc., 5, 188-196, 1962

1963


On multiplication of Cesaro summable series

Joint with Y. Matsuoka

J. London Math. Soc., 38, 393-400, 1963

1964


On absolute Riesz summability factors

Joint with B. L. R. Shawyer

J. London Math. Soc., 39, 455-465, 1964

1965


On strong Riesz summability factors

Joint with B. L. R. Shawyer

J. London Math. Soc., 40, 111-126, 1965

Linear functionals connected with strong Cesàro summability

David Borwein

J. London Math. Soc., 40, 628-634, 1965

On a class of convergent series of positive terms

David Borwein

J. London Math. Soc., 40, 587-588, 1965

1966


On a non-enumerable exceptional set

David Borwein

Amer. Math. Monthly, 73, 288, 1966

On a generalised Cesàro summability method of integral order

David Borwein

Tohoku Math J., 18, 71-73, 1966

On Borel-type methods

Joint with B. L. R. Shawyer

Tohoku Math J., 18, 283-298, 1966

1967


On a method of summability equivalent to the Cesàro method

David Borwein

J. London Math. Soc., 42, 339-343, 1967

On Riesz and generalised Cesàro summability of arbitrary positive order

Joint with D. C. Russell

Math. Z., 99, 171-177, 1967

On Borel-type methods II

Joint with B. L. R. Shawyer

Tohoku Math J., 19, 232-237, 1967

On generalised Cesàro summability

David Borwein

J. Indian Math. Soc., 9, 55-64, 1967

1968


Strong Nörlund summability

Joint with F. P. A. Cass

Math. Z., 103, 94-111, 1968

1969


Multiplication theorems for strong Nörlund summability

Joint with F. P. A. Cass

Math. Z., 107, 33-42, 1969

Scales of logarithmic methods of summability

Joint with R. Phillips

Canad. Math. Bull., 12, 445-452, 1969

A tauberian theorem for Borel-type methods of summability

David Borwein

Canad. J. Math., 21, 740-747, 1969

A property of gradients

Joint with A. Meir

Amer. Math. Monthly, 76, 648, 1969

1970


On Riesz and generalised Cesàro summability

David Borwein

J. London Math. Soc., (2)2, 61-66, 1970

On absolute Borel-type methods of summability

David Borwein

Proc. Amer. Math. Soc., 24, 85-89, 1970

1971


On Abel-type methods of summability,

Joint with J. H. Rizvi

J. Reine Angew. Math, 247, 139-145, 1971

1972


Convergence criteria for bounded sequences

David Borwein

Proc.Edinburgh Math. Soc., (2)19, 99-103, 1972

Divergence criteria for positive series

Joint with A. Meir

Amer. Math. Monthly, 79, 1104-1106, 1972

1973


On strong summability

Joint with J. H. Rizvi

J. Reine Angew. Math, 260, 119-126, 1973

1974


Strict inclusion between strong and ordinary methods of summability

Joint with F. P. A. Cass

J. Reine Angew. Math, 267, 166-174, 1974

Tauberian theorems for Borel-type methods of summability

Joint with E. F. M. Smet

Canad. Math. Bull., 17, 167-173, 1974

1975


A tauberian theorem for Borel-type methods of summability

Joint with I. J. W. Robinson

J. Reine Angew. Math, 273, 153-164, 1975

Generalized strong summability of infinite series

Joint with J. H. Rizvi

J. Reine Angew. Math, 276, 142-147, 1975

1976


Equivalence of Riesz methods of summability

Joint with F. P. A. Cass

J. London Math. Soc., (2)13, 205-208, 1976

A tauberian theorem for Abelian summability methods

Joint with B. B. Watson

J. Reine Angew. Math, 285, 75-76, 1976

On functional Cesàro and Hölder methods of summability

Joint with B. L. R. Shawyer

Canad. J. Math., 28, 1058-1061, 1976

Addendum to "Tauberian theorems for Borel-type methods of summability"

Joint with E. F. M. Smet

Canad. Math. Bull., 19, 245-246, 1976

On the zeros of the power series (...) with an application to discontinuous Riesz-summability

Joint with W. Kratz

Canad. Math. Bull., 19, 417-424, 1976

1977


Tauberian theorems for strong and absolute Borel-type methods of summability

Joint with E. F. M. Smet

Canad. Math. Bull., 20, 161-172, 1977

1978


On certain sequences of plus and minus ones

Joint with W. Gawronski

Canad. J. Math., 30, 170-179, 1978

A sum of reciprocals of least common multiples

David Borwein

Canad. Math. Bull., 20, 117-118, 1978

Tauberian theorems on a scale of Abel-type summability methods

Joint with B. B. Watson

J. Reine Angew. Math, 298, 1--7, 1978

Translates of sequences in sets of positive measure

Joint with S. Z. Ditor

Canad. Math. Bull., 21, 497-498, 1978

The Hausdorff moment problem

Solicited paper

Canad. Math. Bull., 21, 257-265, 1978

1979


Matrix operators on lp,

Joint with A. Jakimovski

Rocky Mountain J. Math, 9, 463-477, 1979

1980


The ultrastructure of monkey foveal photoreceptors, with special reference to the structure, shape, size, and spacing of the foveal cones

Joint with B. Borwein, J. Mederios, and J. McGowan

The American Journal of Anatomy, 159, 125-146, 1980

1981


On the relation between the logarithmic and Borel-type summability methods

Joint with B. B. Watson

Canad. Math. Bull., 24(2), 153-159, 1981

Weighted means, generalised Hausdorff matrices and the Borel property

Joint with F. P. A. Cass

Acta Math. Hung., 37, 29-34, 1981

Tauberian conditions for the equivalence of weighted mean and power series methods of summability

David Borwein

Canad. Math. Bull., 24, 309-316, 1981

Matrix transformations of weakly multiplicative sequences of random variables

David Borwein

J. London Math. Soc., 23, 363-371, 1981

Generalization of the Hausdorff moment problem

Joint with A. Jakimovski

Canad. J. Math., 33, 946-960, 1981

Generalization of the Hausdorff moment problem. Proceedings of International Conference on Nonlinear Analysis and Applications, St. John's, Newfoundland

Joint with A. Jakimovski

Nonlinear Analysis and Applications, na, 33-37, 1981

1982


Tauberian theorems between the logarithmic and Abel-type summability methods

Joint with B. B. Watson

Pacific J. Math., 101, 11--23, 1982

On summability factors for the strong Cesàro method for integrals

Joint with K. Roberts

Analysis, 2, 7--42, 1982

1983


Transformations of certain sequences of random variables by generalized Hausdorff matrices

Joint with A. Jakimovski

Pacific J. Math., 107, 1, 15-26, 1983

Generalized Hausdorff matrices as bounded operators on lp

David Borwein

Math. Z., 183, 483-487, 1983

1984


Nörlund matrices as bounded operators on lp

Joint with F. P. A. Cass

Arch. Math., 42, 464-469, 1984

1985


Conditions for inclusion between Nörlund summability methods

Joint with B. Thorpe

Acta Math. Hung., 45, 1-2, 151-158, 1985

Convergence of lattice sums and Madelung's constant

Joint with J. M. Borwein and K. F. Taylor

J. Math. Phys, 26(11), 2999-3009, 1985

1986


On Cesàro and Abel summability factors for integrals

Joint with B. Thorpe

Canad. J. Math., 38, 2, 453-477, 1986

On absolute generalized Hausdorff summability

Joint with F. P. A. Cass and J. E. Sayre

Arch. Math., 46, 419-427, 1986

A note on alternating series in several dimensions

Joint with J. Borwein

Amer. Math. Monthly, 93, 7, 531-539, 1986

On generalized Hausdorff matrices

Joint with F. P. A. Cass and J. E. Sayre

J. Approx. Theory, 48, 4, 354-360, 1986

1987


A Tauberian theorem concerning weighted means and power series

Joint with A. Meir

Proc. Camb. Phil. Soc., 101, 283-286, 1987

Tauberian and other theorems concerning Dirichlet's series with non-negative coefficients

David Borwein

Proc. Camb. Phil. Soc., 102, 517-532, 1987

1988


A Tauberian theorem concerning Borel-type and Cesàro methods of summability

Joint with T. Markovich

Canad. J. Math., 40, 1, 228-247, 1988

On Cesàro and Borel-type summability

Joint with T. Markovich

Proc. Amer. Math. Soc., 103, 4, 1108-1112, 1988

1989


Enumeration of injective partial transformations

Joint with S. A. Rankin and L. E. Renner

Discrete Math., 73, 291-296, 1989

On strong generalized Hausdorff summability

Joint with F. P. A. Cass and J. E. Sayre

Acta Math. Hung., 53, 1-2, 95-101, 1989

On relations between weighted mean and power series methods of summability

Joint with W. Kratz

J. Math. Analysis and Applications, 139, 1, 178-186, 1989

A Tauberian theorem concerning Dirichlet series

David Borwein

Proc. Camb. Phil. Soc., 105, 481-484, 1989

1988


Energy of static electron lattices

Joint with J. M. Borwein, R. Shail, and I. J. Zucker

J. Math. Phys, 21, 1519-1531, 1988

1989


Analysis of certain lattice sums

Joint with J. M. Borwein and R. Shail

J. Math. Analysis and Applications, 143, 1, 126-137, 1989

Tauberian theorems concerning Laplace transforms and Dirichlet series

David Borwein

Arch. Math., 53, 352-362, 1989

1990


An inclusion theorem for Dirichlet series

David Borwein

Canad. Math. Bull., 32(4), 479-481, 1990

Asymptotic relationships between Dirichlet series

David Borwein

J. Math. Analysis and Applications, 147, 2, 604-609, 1990

1991


Fixed point iterations for real functions

Joint with J. Borwein

J. Math. Analysis and Applications, 157, 1, 112-126, 1991

The non-local nature of the summability of Fourier series by certain absolute Riesz methods

David Borwein

Israel Mathematical Conference Proceedings, 4, 69-72, 1991

1992


Weighted means and summabiltiy by the circle and other methods

Joint with T. Markovich

J. of Approximation Theory, 68, 1, 49-55, 1992

The non-local nature of the summability of Fourier series by certain absolute Riesz methods

David Borwein

Proc. Amer. Math. Soc., 114, 1, 89-94, 1992

A Tauberian theorem concerning Borel-type and Riesz summability methods

David Borwein

Canad. Math. Bull., 35(1), 14-20, 1992

Tauberian theorems concerning power series with non-negative coefficients

David Borwein

Acta Mathematica Hungarcia, 59, 1-2, 85-89, 1992

1993


Nörlund operators on lp

David Borwein

Canad. Math. Bull., 36, 1, 8--14, 1993

Generalized Hausdorff and weighted mean matrices as operators on lp

Joint with X. Gao

J. Math. Analysis and Applications, 178, 517-528, 1993

1994


An O-Tauberian theorem and a high indices theorem for power series methods of summability

Joint with W. Kratz

Proc. Camb. Phil. Soc., 115, 365-375, 1994

Weighted means and summability by generalized Nörlund and other methods

Joint with R. Kiesel

J. Math. Analysis and Applications, 184, 607-619, 1994

Matrix operators on lp to lq

Joint with X. Gao

Canad. Math. Bull., 37, 4, 448-456, 1994

Matrix transformations of power series

Joint with A. Jakimovski

Proc. Amer. Math. Soc., 122, 2, 511-523, 1994

On some trigonometric and exponential lattice sums

Joint with J. Borwein

J. Math. Analysis and Applications, 188, 1, 209-218, 1994

1995


On an intriguing integral and some series related to zeta(4)

Joint with J. Borwein

Proc. Amer. Math. Soc., 123 (4), 1191-1198, 1995

Explicit evaluation of Euler sums

Joint with J. Borwein and R. Girgensohn

Proc.Edinburgh Math. Soc., 38, 277-294, 1995

Matrix transformations of series of orthogonal polynomials

Joint with P. Borwein and A. Jakimovski

Mathematika, 42, 427-443, 1995

1996


Giuga's conjecture on primality

Joint with J. Borwein, P. Borwein, and R. Girgensohn

Amer. Math. Monthly, 103(1), 40-50, 1996

Approximate subgradients and coderivatives in Rn

Joint with J. Borwein and X. Wang

Set- Valued Analysis, 4, 375-398, 1996

1998


Convergence of Madelung-like lattice sums

Joint with J. Borwein and C. Pinner

Trans. Amer. Math. Soc., 350, 3131-3167, 1998

Simple conditions for matrices to be bounded operators on lp

David Borwein

Canad. Math. Bull., 41, 10--14, 1998

A generalization of Hardy's inequality with applications

Joint with A. Jakimovski

Communications in Applied Analysis, 2, 309-320, 1998

A high indices Tauberian theorem

Joint with W. Kratz

Szeged, 64, 143-149, 1998

Matrices that commute with certain Hausdorff matrices

Joint with A. Jakimovski

Analysis, 18, 227-244, 1998

1999


Two Tauberian theorems for Dirichlet series methods of summability

Joint with J. Beurer and W. Kratz

Acta. Sci. Math., 65, 139-168, 1999

2000


Weighted mean operators on lp

David Borwein

Canad. Math. Bull., 43, 406-412, 2000

Surprize maximization

Joint with J. Borwein and P. Marechel

Amer. Math. Monthly, 107, 517-527, 2000

2001


Some remarkable properties of sinc and related integrals

Joint with J. Borwein

Ramanujan, 5, 73-89, 2001

One-sided Tauberian theorems for Dirichlet series methods of summability

Joint with W. Kratz and U. Stadtmoller

Rocky Mountain J. Math, 31, 797-830, 2001

Refined convexity and special cases of the Blaschke-Santalo inequality

Joint with J. Borwein, G. Fee, and R. Girgensohn

Math. Inequalities and Applications, 4, 631-638, 2001

A miscellany for mathematicians and others

Robin Wilson and Jeremy Gray

Mathematical Intelligencer , na, 3--4, 2001

2002


Multi-variable sinc integrals and volumes of polyhedra

Joint with J. Borwein and B. A. Mares Jr.

Ramanujan, 6, 189-208, 2002

2004


A one-sided Tauberian theorem for the Borel summability method

Joint with W. Kratz

J. Math. Analysis and Applications, 293, 285-292, 2004

Finding and excluding $b$-ary Machin-type individual digit formulae

Joint with J. Borwein and W. F. Galway

Canad. J. Math., 56, 897-925, 2004

Meandering in Euler's neighbourhood

Julian Havel

CMS Notes, na, 6--7, 2004

2005


Weighted convolution operators on $\ell_p$

Joint with W. Kratz

Canad. Math. Bull., 48, 175-179, 2005

A century of developments

Jacob Korevaar

Bull Amer. Math. Soc, 42, 401-406, 2005

2006


Parametric Euler sum identities

Joint with D. M. Bradley and J. Borwein

J. Math. Analysis and Applications, 316, 328-338, 2006

2007


On the dynamics of certain recurrence relations

Joint with J. Borwein, R. Crandell, and R. Mayer

Ramanujan, 13, 63-101, 2007

Van der Pol expansions of L-series

Joint with J. Borwein

Canad. Math. Bull., 50, 11--23, 2007

Hypergeometric forms for Ising-class integrals

Joint with D. H. Bailey, J. Borwein, and R. E. Crandall

Experiment. Math., 16, 257-276, 2007

2008


The evaluation of Bessel functions via exp-arc integrals

Joint with J. Borwein and O-Y. Chan

J. Math. Analysis and Applications, 341, 888-901, 2008

Effective Laguerre asymptotics

Joint with J. Borwein and R. E. Crandall

SIAM J. Numer. Anal., 46, 3285-3312, 2008

Surprising sinc sums and integrals

Joint with J. Borwein and R. Baillie

Amer. Math. Monthly, 115, 888-901, 2008

2010


$L_p$-norms and the sinc function

Joint with J. Borwein and I. E. Leonard

Amer. Math. Monthly, 117, 528-539, 2010

2011


Moments of Ramanujan's generalized elliptic integrals and extensions of Catalan's constant

Joint with J. Borwein, M. L. Glasser, and J. G. Wan

Journal of Mathematical Analysis and Applications, 384, 478-496, 2011

2012


Log-sine evaluations of Mahler measures II

Joint with J. Borwein, J. G. Wan and A. Straub

Integers, 12A, #A5, 2012

On formulas for $\pi$ experimentally conjectured by Jauregui-Tsallis

Joint with T. Amdeberhan, J. Borwein and A. Straub

Journal of Mathematical Physics, 53, 073708, 2012

A Sinc that Sank

Joint with J. Borwein and A. Straub

American Mathematical Monthly, 119, 535-549, 2012

2013


Criteria for the Sequence of Differences of a Bounded Sequence to be Null

David Borwein

Bulletin of the Australian Mathematical Society, doi:10.1017/S000497271200072X, 2012

2014


On lattice sums and Wigner limits

Joint with J. Borwein and A. Straub

J Math Anal and Appl, 414(2), 489-513, 15 June 2014 [in press]

On the Solution of Linear Mean Recurrences

Joint with J. Borwein and B. Sims

Amer. Math. Monthly, 121, 486-498, 2014